Playoff Probabilities Simulation - PECOTA Edition
by stevesommer05 on Feb 11, 2010 8:00 AM EST
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PrintWith some of the projection systems also coming out with projections of the standings now's probably a good time to attach some playoff probabilities to the projections. I'll start with PECOTA.
My methodology is fairly simple. I created a Monte Carlo simulation that modeled team wins as a normal random variable with a mean of the projected wins and a variable standard deviation (not variable within a set of simulation runs but across unique sets of runs).
I ran the simulation using a 9 win SD, an 8 win SD, and an 8 win SD with the caveat that total team wins had to fall within projected + or - 20.
The results using a 9 win standard deviation are after the jump and a spreadsheet containing all of the results is linked at the end.
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| New York Yankees | 94 | 68 | 41% | 25% | 66% |
| Boston Red Sox | 92 | 70 | 31% | 25% | 56% |
| Tampa Bay Rays | 90 | 72 | 23% | 23% | 46% |
| Baltimore Orioles | 80 | 82 | 4% | 7% | 11% |
| Toronto Blue Jays | 72 | 90 | 1% | 1% | 2% |
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| Minnesota Twins | 83 | 79 | 37% | 2% | 39% |
| Chicago White Sox | 80 | 82 | 24% | 2% | 26% |
| Detroit Tigers | 78 | 84 | 17% | 2% | 19% |
| Cleveland Indians | 76 | 86 | 12% | 1% | 13% |
| Kansas City Royals | 75 | 87 | 10% | 1% | 11% |
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| Texas Rangers | 87 | 75 | 47% | 3% | 50% |
| Los Angeles Angels | 80 | 82 | 20% | 3% | 23% |
| Oakland Athletics | 80 | 82 | 20% | 3% | 23% |
| Seattle Mariners | 77 | 85 | 13% | 2% | 15% |
A few quick bullet points
- The East is pretty good eh? 81% of the time the wild card came from there.
- Raise your hand if you would have pegged the Royals for having only a 4% less chance to make the playoffs than the Mariners. Yeah thought so. Granted is that just PEOCTA underrating the M's?
- The Central is pretty jumbled up, and those teams don't project to have the wild card to fall back on like the East
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| Philadelphia Phillies | 88 | 74 | 45% | 9% | 54% |
| Atlanta Braves | 83 | 79 | 22% | 9% | 31% |
| Florida Marlins | 81 | 81 | 16% | 7% | 23% |
| New York Mets | 79 | 83 | 11% | 5% | 16% |
| Washington Nationals | 76 | 86 | 6% | 3% | 9% |
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| St. Louis Cardinals | 84 | 78 | 33% | 6% | 39% |
| Cincinnati Reds | 82 | 80 | 25% | 5% | 30% |
| Chicago Cubs | 79 | 83 | 15% | 4% | 19% |
| Milwaukee Brewers | 79 | 83 | 15% | 4% | 19% |
| Houston Astros | 76 | 86 | 9% | 3% | 12% |
| Pittsburgh Pirates | 70 | 92 | 3% | 1% | 4% |
| W | L | Div Win% | WC% | Playoff % | |
|---|---|---|---|---|---|
| Arizona Diamondbacks | 87 | 75 | 34% | 12% | 46% |
| Colorado Rockies | 86 | 76 | 29% | 12% | 41% |
| Los Angeles Dodgers | 83 | 79 | 19% | 10% | 29% |
| San Francisco Giants | 82 | 80 | 16% | 9% | 25% |
| San Diego Padres | 71 | 91 | 2% | 1% | 3% |
More bullet points
- The West should be fun division to watch
- The Phillies were the only team to break a 50% chance, and that's with a pessimistic Braves projection (clearly just my opinion)
Next up, I'll do the same with CHONE.
Complete results can be found here
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As a Twins fan,
what gets me isn’t the 83-win division crown. It’s that, somehow, no team in the AL Central wins fewer than 75 games.
I’m also really surprised at the Mariners totals.
Steve, how easy is it to show what percentage of the time an AL Central team wins fewer than 75 games.
I’m guessing it’s 90%.
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Pretty simple
If I had my data in front of me. Which I won’t until I get home. I’d guess it’s pretty often too.
by stevesommer05 on Feb 11, 2010 9:33 AM EST up reply actions
I'd also be interested to see the average number of wins for each place in the standings by division, including wild card winner.
Again, probably going to be more spread out. Yankees predicted to be the best team in AL East and average 94 wins, but I would bet that AL East division winner averages more like 96-98 wins. And it’ll take more than 92 wins, on average, to win the AL Wild Card.
Would also be cool to do with leader boards, as an example for the “nobody’s going to hit 40 HRs!” crowd. Show both the projections for the top 10 HR hitters and then the average leader board 1-10, ignoring who hit that many HRs.
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by Sky Kalkman on Feb 11, 2010 12:40 PM EST up reply actions
That's the beauty of regression to the mean.
I can tell you that, given these projections, we can certainly expect an AL Central team to finish at 70 wins or below (not to say it’s certain, but it’s a reasonable expectation). What we don’t know right now is which. We can say that the Royals are the most likely, the Tigers somewhat less likely and the Indians somewhat less likely.
And we probably can a team around 90 wins also.
The chances of the division being won by 83 games are really slim.
"Pinch-bunters don't have a ton of value, even with the Twins"
by Steven Ellingson on Feb 11, 2010 10:33 PM EST up reply actions
I'm surprised that PECOTA likes Texas so much
presumably that’s because of the run prevention, with the additions of Colby Lewis and Rich Harden, as well as potential full seasons from Derek Holland and Neftali Feliz.
I also would’ve expected St. Louis and Atlanta to be better, too.
I like baseball.
I write for Beyond the Box Score and The Hardball Times Fantasy
Well, it likes them to repeat their win total from an unflukey season last year.
That’s with Kinsler having a down year offensively last year (though an up year defensively); Hamilton and Davis failing in large ways at the plate in ’09; Holland, Hunter, Borbon, Feliz having second seasons after solid-to-great debuts; replacing Kevin Millwood with Colby Lewis, Rich Harden with Vicente Padilla and Hank Blalock with Vladimir Guerrero.
I don’t think it’s particularly positive (or negative, btw).
Hot damn
I can’t believe that PECOTA hates the NL Central that much. 84 wins?
In football, the object is for the quarterback, otherwise known as the field general, to be on target with his aerial assault, riddling the defense by hitting his recievers with deadly accuracy in spite of the blitz, even if he has to use the shotgun. With short bullet passes and long bombs, he marches his troops into enemy territory, balancing this aerial assault with a sustained ground attack that punches holes in the forward wall of the enemy's defensive line.
In baseball the object is to go home! And to be safe! "I hope I'll be safe at home!"
-George Carlin (RIP)
The question I have with these Win predictions is
Is the imput static ?
So you get a number of outcomes given static imputs and you can predict 1std above and below average expected wins.
Or does one also model uncertainty aroudn the imputs.
I.e. one player’s woba+ may be 350, but reasonably it’s somewhere between 370 and 330. Same with games played, etc.
I can only hope that the Rangers beat their PECOTA projections again.
That would make my year.
I’m hoping 95 wins. Not that that’s a realistic wish by any definition of the word “realistic”.
Question
Each time you run a season do the win and loss totals match? Are you just taking the Pecota win prediction totals and using a random number generator along with their distribution of total wins probability curve to come up with a seasonal win total – then repeating this step X number of times? Just curious as to the exact methodology.
Given all the problems Pecota had putting their team win/loss projections out – I will await the other systems like CHONE.
vr, Xei
due to massive laziness
it’s the former. Extremely simplistic, but probably gets at the final answer pretty well. I’ll probably post process to answer some of Sky’s questions above
by stevesommer05 on Feb 11, 2010 9:00 PM EST up reply actions
oops need to read more carefully
I guess it was the latter :) The win totals don’t match directly out of the sim… would have to post process like I mentioned
by stevesommer05 on Feb 11, 2010 9:03 PM EST up reply actions
Why does the East projection
for TB, New York, and Boston seem just a tad depressed, to me?
by FloridaownsFSU on Feb 11, 2010 10:03 PM EST reply actions
Not Quite How I'd Have Done It...
I think it’s fine to use a normal distribution with some standard deviation to handle the true talent. However, I think once you do that you still want to handle the uncertainty in actual performance. If it’s not clear what I’m saying, let’s look at an example team: my Pirates. PECOTA has them at 70 wins, so we say that is their mean true talent. Their actual true talent might be sampled from a normal distribution with a mean of 70 and a standard deviation of say 9 wins. So in some runs their true talent may be say 79 wins, but that doesn’t mean they will win 79 games. In seasons where they have a true talent of 79 wins they might not actually win that number of games…they could win more or less so we would want to use some sort of sampling technique for this as well. Oddly enough in some runs they will have 79-win talent and only win say 70 games while in other runs they will have 70-win talent and might win 79 or more games.
If you want simplicity then you can handle this with the binomial distribution of 162 trials for each team given their talent in that run. However, that has issues including that it doesn’t guarantee the wins add up. You could simulate each game of the season if you want where you use a log5 type matchup based on their true talents in that run. I believe this is similar to what Rally does in his CHONE standings projections. I’m not sure how much more accurate this technique would be, but it seems to me to be purer.
Good points
This was a crude quick way to do it, but I think that it gives a decent answer despite its shortcomings. Regards to your first point about true talent level, I think it would likely come out in the wash as your final sentence alludes to (granted that depends on your choice of distributions for each). My gut thought is that doing something like that would be similar to running what I did with a wider variance.
As regards to your second paragraph, I’d like to incorporate log5 and use Rally’s method. That’s the next step for me I think. Thanks for the input.
by stevesommer05 on Feb 12, 2010 8:59 AM EST up reply actions
I would say that the chance a non-AL East team gets the wild card is even less than 19% in fact
I’d say that perhaps closer to 5-10% of the time a non-AL east team gets it
by benderbrodriguez on Feb 20, 2010 12:32 PM EST reply actions
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